Polaroid type operators under perturbations
Tom 214 / 2013
Studia Mathematica 214 (2013), 121-136
MSC: Primary 47A10, 47A11; Secondary 47A53.
DOI: 10.4064/sm214-2-2
Streszczenie
A bounded operator $T$ defined on a Banach space is said to be polaroid if every isolated point of the spectrum is a pole of the resolvent. The “polaroid” condition is related to the conditions of being left polaroid, right polaroid, or $a$-polaroid. In this paper we explore all these conditions under commuting perturbations $K$. As a consequence, we give a general framework from which we obtain, and also extend, recent results concerning Weyl type theorems (generalized or not) for $T+K$, where $K$ is an algebraic or a quasi-nilpotent operator commuting with $T$.